Solve Square Root Problems

Solve Square Root Problems-63
Let's use this example problem to illustrate the general steps for adding square roots.

Let's use this example problem to illustrate the general steps for adding square roots.

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Because radical signs are not always easy to produce on demand, another way to write "the square root of x" is to use an exponent: x Most square roots are irrational numbers.

This means that not only are they not nice, neat integers (e.g., 1, 2, 3, 4 . .), but they also cannot be expressed as a neat decimal number that terminates without having to be rounded off. So even though 2.75 is not an integer, it is a rational number because it is the same thing as the fraction 11/4.

In the example below, notice that completing the square will result in adding a number to both sides of the equation—you have to do this in order to keep both sides equal!

Can you see that completing the square in an equation is very similar to completing the square in an expression?

You'll see more on this in the section about graphs later, but as a rough example, you have already observed that the square root of 100 is 10 and the square root of 0 is 0.

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On sight, this might lead you to guess that the square root for 50 (which is halfway between 0 and 100) must be 5 (which is halfway between 0 and 10).

Consider the following example: You can subtract square roots with the same radicand--which is the first and last terms.

Let's look at the following example You may immediately see the problem here: The radicands are not the same. However, if we simplify the square roots first, we will be able to add them.

The square root of a number is a value that, when multiplied by itself, gives the original number.

For example, the square root of 0 is 0, the square root of 100 is 10 and the square root of 50 is 7.071. Problems involving square roots are indispensable in engineering, calculus and virtually every realm of the modern world.

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